The principal contribution of this paper is *not* a first-principles derivation of the fine-structure constant α, but rather a *computational motivation* for the metric signature (5, 2) underlying Wyler's 1969 geometric formula D₅ = SO₀ (5, 2) /SO (5) ×SO (2). We introduce an axiomatic computational framework that models every physical change as a Compare-And-Swap (CAS) operation — four explicit axioms plus one lemma (together with two working definitions, four framework-internal meta-rules, and two external assumptions; thirteen items in total, disclosed in §3. 1) — and prove (Theorem 1, qualified as a Structural Proposition) that the irreversible/reversible classification of cost corresponds structurally to the positive/negative signs of a quadratic form. Among the eight possible sign partitions of the seven macroscopic degrees of freedom (four domain axes plus three CAS stages), (5, 2) is the unique admissible partition; other simple Lie groups of the same dimension 21, namely SO (7) and SO (4, 3), are explicitly excluded on categorical grounds. The framework-internal status of the Wyler formula factors is honestly classified: 9 is self-derived from the framework cost accounting; π⁵/ (2⁴·5!) is directly identical to the Hua volume of the type IV₅ Lie ball (Hua 1963, Ch. IV §1. 4 Theorem 1. 1. 2) — and since Theorem 1 forces SO₀ (5, 2) → D₅, this factor carries a framework-internal motivation; the denominator 8π⁴ and the 1/4 exponent are classified as borrowings from the Wyler–Robertson reformulation (the 1/4 exponent is independently rediscovered via the framework's cost-ratio interpretation, but an axiom-level derivation is left for future work). Result: 1/α = 137. 036082, with a relative deviation of 6×10^-7 from the CODATA value. A different combination of structural constants in the same axiomatic system yields the Weinberg angle sin²θW = 7/ (2+9π) = 0. 23122, agreeing with the MS-bar value at the MZ scale (the agreement of the renormalization scheme is stated as a conjecture). All five steps of the derivation are framework-internal forward chains, forced by the framework's two-reading principle (cost reading vs norm reading) plus standard arithmetic. The internal degree count 7 = 4+3 (four domain axes + three CAS stages) coincides structurally with the classical Hamming code 7, 4, 3 decomposition (four message bits + three parity bits) ; the quantum Steane code [7, 1, 3] is a CSS construction built on this Hamming code, and is noted as a quantum lift rather than a direct correspondence. The baryon-to-photon ratio ηB = 6. 14×10^-10 is computed from the two framework-derived quantities alone (α and sin²θW) and agrees with the Planck 2018 measurement (6. 12 ± 0. 04) ×10^-10 to within 0. 4σ. The framework-internal mechanisms supporting this estimate (the 1/π RLU identification ratio, the prefactor 2 from meta-level orthogonality) are explicitly designated as a working hypothesis (RLU coupled-access regime), falsifiable by future CMB precision measurements. The genuinely new contributions of this paper are: (i) the correspondence between cost classification and metric signature (Structural Proposition 1) ; (ii) the simultaneous framework-internal production of α and sin²θW from the same axiomatic system; and (iii) the structural match between the seven internal degrees of freedom and the Hamming code. We position the framework as a third, cost-theoretic branch of the axiomatic-reconstruction tradition, lying alongside the full-reconstruction school of Hardy 2001 / CDP 2011 and the partial-reconstruction school of Spekkens 2007 / Masanes–Müller 2011 / Pawlowski 2009. This v2. 0 record contains both the English version (alpha137ₑn. pdf, primary, 44 pages) and the Korean version (alpha137ₖr. pdf, 35 pages).
Hyunjin Han (2026) studied this question.